The trouble with factors

Factor investing is hot these days. Invesco recently documented the rise of "smart beta" ETFs at ETF.com:

Overall, smart-beta ETFs accounted for over 17% of U.S. ETF net inflows in 2014, despite representing less than 11% of the total assets. Today there are more than 350 smart-beta ETFs available in the U.S. comprising over $230 billion in AUM, up from just 212 products and $64.8 billion in 2010.1 Over the past year, institutional decision-makers—including public and private pensions, endowments and foundations, and registered investment advisors who manage institutional assets—have become more familiar with the smart-beta category.

The article explained that "smart beta" funds really represent a form of factor investing, with factors in use such as low vol, dividend yield, fundamental weight, which is a form of value tilt:

In the simplest terms, smart-beta ETFs follow indexes based on alternative weighting methodologies. Many of these alternative weighting methodologies (such as low volatility, high dividend and fundamentally weighted) have historically delivered favorable risk-adjusted returns and varying returns across different market regimes. As a result, institutions are increasingly looking to smart-beta ETFs as a complement to and a replacement for both their traditional market-cap-weighted ETFs and their actively managed positions.

Portfolio construction with factors
In addition to using factors at the stock portfolio level, factor investing has migrated to portfolio construction. A participant at the recent Sixth Annual Southeast Asia Institutional Investment Forum revealed how some institutions had adopted the risk factor allocation as a substitute for asset allocation in their portfolios:

What’s the secret sauce for making a multi-asset strategy successful? This past December, in Singapore, I asked the speakers on my panel at the Sixth Annual Southeast Asia Institutional Investment Forum and their answers all shared one thing in common: risk factor allocation.

Some examples of techniques used by some very large institutions:

Chiew Kit Tham, managing director at GIC, told the conference participants that they have pared back the number of asset classes in their program from 39 to six for this reason. GIC is a sovereign wealth fund set up by the Singapore government and manages hundreds of billions of the country’s foreign reserves. Instead of asset classes, GIC now focuses on a set of factors that they want to be exposed to: equity risk with a bias towards emerging markets growth equities, real estate, and private equity. They consider these the main drivers of their portfolio risk and return. Secondary drivers include factors such as momentum, size, value, credit, and carry.

Richard Brandweiner, CFA, CIO of First State Super, added that they have also shifted attention away from asset classes. “Benchmarks asset classes are quite arbitrary and are increasingly less relevant. We focus on what systemic exposures we try to capture with a certain asset class and target a portfolio with the desired mix of exposures,” said Brandweiner.

In a similar vein, Nachcha Protpakorn, deputy secretary general of the US$20 billion Thai Government Pension Fund (GPF) discussed their focus on long-term macroeconomic drivers. She believes the practice allows them to take advantage of shorter-term opportunities without wandering too far away from the long-term policy portfolio.

In effect, these institutions are moving towards the Norway model, which is an approach pioneered by Norges Bank Investment Management (NBIM). Such an approach requires a shift in thinking about overall portfolio construction. Instead of thinking about assets and their characteristics, these investors now focus on the factor characteristics and factor risk premiums.

The shift from asset classes to factors requires changes in the portfolio construction process.

For example, target allocations to specific asset classes become an afterthought. Brandweiner’s advice: “Avoid silos in thinking. Think of portfolio construction from a factor perspective, such as duration, credit, and currency. There is no bucket for a particular private equity or infrastructure fund but think of their contribution as a group.”

Tham gave a similar example: To add high yield to a portfolio, an investor will need to reduce exposures to the equity and credit factors. Similarly, there will be no target allocation to active and passive components of the portfolio.

These components are switchable in terms of exposures to factors. Once appropriate funds are identified based on their risk-return trade-offs, etc., allocations can then be set in line with their factor exposures. Tham highlighted a case where they would sell the “policy portfolio” to make room for the new active funds added.

The trouble with factors
While I appreciate the different perspective that factor investing contributes, it doesn't represent the Holy Grail of Investing. Replacing asset exposures with factor exposures at a portfolio level has the benefit of changing the way of thinking to a macro mindset, which can be helpful for the right kind of organization, it is unclear to me whether such a shift actually raises returns or reduces risk.

I recently encountered MIT Sloan Research Paper No. 5128-15, entitled Facts About Factors, by Paula Cocoma, Megan Czasonis, Mark Kritzman and David Turkington. Here is the abstract:

It has become fashionable to allocate portfolios to factors rather than to assets. The often stated motivation for this approach is that factors are less correlated with each other than assets; therefore, factors afford greater opportunity for diversification. This argument is specious, of course, because ultimately the portfolio must be invested in assets. It is, therefore, impossible to produce a better in-sample portfolio by describing the portfolio as a set of factors than assets. There are several potentially legitimate arguments, though, for favoring factor stratification over asset stratification. It could be that factors are easier to forecast than assets, because investors are better able to relate current information to future factor behavior than to future asset behavior. Unfortunately, we have no way of testing this conjecture generically. But there are several testable conjectures. Perhaps risk estimated from high-frequency returns predicts risk over longer horizons more reliably for factors than for assets. Or the statistical properties of large samples may predict the statistical properties of small samples more reliably for factors than for assets. Or, for the same sample size, the statistical properties of factors may be more stationary from one sample to the next than they are for assets. Finally, it may be that reducing the dimensionality of a large set of assets to a smaller set of factors reduces noise more effectively than reducing dimensionality to a smaller set of assets. We offer empirical evidence of the validity, or lack thereof, of these testable conjectures.

The main conclusions of the research says that it's hard to prove that there is an added benefit of factor based portfolio construction:

Some investors propose using factors instead of assets as the building blocks for forming portfolios, because factors appear to be less correlated with each other than assets
and thus seem to afford greater potential for diversification. These ostensibly low correlations, however, reflect the fact that the asset combinations used to mimic factors include short positions in some of the assets and not superior diversification opportunities. We have shown that it is impossible to generate a superior in‐sample portfolio, given the same constraints, by regrouping assets into factors if the investable units are assets from which the factors are formed.

We also considered the possibility that investors are more skilled at relating current information to future factor behavior than to future asset behavior. However, we conceded that we could not test this conjecture generically, because skill is investor‐specific.

However, we did test whether the statistical properties of factors are more stationary than the statistical properties of assets. We found no evidence that factors produce more stable results across varying frequencies, nor from large samples to small samples, nor across independent samples. On the contrary, we found evidence of the opposite, on average.

Finally, we tested whether reducing the dimensionality of a larger set of assets to a smaller set of factors reduces noise more effectively than reducing the dimensionality to a smaller set of assets. Again, we found no evidence that factors are meaningfully more effective than assets at noise reduction.

Bottom line, it's a useful approach but it's not the Holy Grail:

Where does this leave us? In our view, the case is yet to be made that investors should use factors as building blocks for forming portfolios rather than assets. We do believe,
however, that investors may be able to gather useful insights about the performance of their portfolios by attributing performance to factor exposures in addition to asset exposures. And we believe as well that investors may be able to manage risk more effectively by considering a portfolio’s factor exposures in combination with its asset exposures. Beyond these applications, investors must decide for themselves whether they have greater conviction about future factor behavior or future asset behavior.

The challenges of stock based factor investing
When I think about factor based stock investing, or "smart beta" funds, a number of issues come up. Before I do, let me explain the typical steps taken to calculate factor exposures and returns:

1. Condition the factor, or scrub the data: Supposing that your "factor" is E/P, or the inverse of the P/E ratio (as sorting on E/P deals with negative earnings properly). You might want to throw out any companies with an E/P of more than 50% (or P/E less than 2) as bad data. If your factor is Size, quants often condition on log(market cap) in order to build a better linear relationship.
2. Calculate the Z-score: Z = (Conditioned factor - Sample average) / Sample standard deviation
3. Calculate the factor return for a single period: Regress the excess return of a group of stocks to the Z-score exposure of those stocks.
4. Repeat steps 1 to 3 for factor returns for other periods.

Having done the messy part of performing factor analysis myself, a number of problems arise with using factors to generate stock level alpha.

• "Smart beta" single factor portfolios are so 1970s. The idea of factor exposures came from academic research done in the 1970s as a way of investigating the Efficient Market Hypothesis. If the market is efficient, as the theory goes, then you shouldn't be able to construction portfolios with market betas equal to the market with better than market returns. Thus, a number of academics found a whole slew of "anomalies", such as the small cap anomaly (or factor), the low P/E anomaly, the low P/B anomaly and so on. In the late 1970s and early 1980s, a number of institutions created mandates for quantitative money managers to invest based on these factors, which we mostly know as value factors today. Sophisticated quant managers have moved on from single factor portfolios and I explain some of the other techniques used by quants today below. Somehow, what was a very old single factor idea has become new again, largely because of marketing hype.
• How stable are factor returns and "anomalies"? That's a good question. Cullen Roche recently wondered out loud if there are any reliable factors. That is a problem that all quants face. A 2003 paper by Motohiro Yogo entitled "A consumption based explanation of expected stock returns" found that value and size factors were highly pro-cyclical. Value and small caps tended to perform well in economic expansions and underperformed during recessions. Since the economy spent more time in expansion, it could account for the value and size effect found in the anomalies literature. I would also note that one of the results from the MIT paper was:

We found no evidence that factors produce more stable results across varying frequencies, nor from large samples to small samples, nor across independent samples. On the contrary, we found evidence of the opposite, on average.

• Do you use naive or pure factors? Supposing that you were using E/P as a factor. Would you rank E/P across all stocks in the market (naive), or would you rank them on a sector or industry neutral basis, which is a "pure" factor return? In my experience, using the "pure" factor approach creates a number of problems. First, the magnitude of the factor alpha falls as the number of sectors and industry rise, indicating that the factor is capturing a sector or industry alpha rather than a stock alpha. Second, slicing and dicing by too many industries creates a problem of some industries with a sample size problem. How confident can you be of a statistical and quantitative approach to factor investing if there are only 3 or 5 stocks in your industry sample?
• Should you customize factor exposure by sector or industry? A typical "smart beta" fund will apply a single factor across all sectors of the market. For example, a fundamentally weighted fund using sales as a weighting factor would weight positions by sales instead of market cap. Such an approach is equivalent to using Price to Sales as a factor to derive alpha and control risk. But fundamental sector analysts will tell you that Price to Sales may not make sense for certain sectors. For example, what bank analyst uses "sales" as a metric? On the other hand, growth stocks trade on momentum factors and applying a value measures like Price to Sales to a growth stock universe will give you a portfolio concentrated on failed growth stories. Intelligent investors know that certain metrics are appropriate for certain sectors and industries and inappropriate for others. 
• Factor returns are not linear. Recall how factor returns are calculated. You regress the excess return of a group of stocks to the Z-score of factor exposure for those stocks. The underlying assumption is that, on average, the returns to a factor are roughly linear and are well behaved and there are no severe twists in the return distribution. Imagine an example where the factor is Size, or market cap. During a single period, large caps returns are roughly zero, medium caps returns are very high and small caps are negative. A linear regression will its best try fit a straight line to that relationship. In our example, the returns to Size (market cap) is then positive because of the large outperformance of medium cap stocks. In real-life, these kinds of U-shaped distributions in factor returns happen all the time. On the other hand, if a portfolio is weighted in mainly large cap stocks, its performance will be very different to the Size factor return because of the skew in the data. Now try explaining that to your client.

Now that I have thoroughly trashed factor analysis, it doesn't mean that it doesn't have its place in quantitative investing. Investors need to go beyond the marketing hype and understand how factors are constructed, how a portfolio is formed using factor analysis and the limitations of that approach.

Don't just believe the backtests. Your own mileage will vary.